Finite Group Databasebeta

← #11789902

Subgroups — #11789902

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63648C211yesmaximal, characteristic
2C2×C3×#815C211yesmaximal, characteristic, complemented
3#10591352C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5C2×#63564C211yesmaximal, characteristic
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69818—31nomaximal
9#68857—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×Dic3⋊Dic3—21no—
18C2×#3722—21no—
19C2×#3722—21no—
20#63648—22no—
21C3×#815—22no—
22#63579—21no—
23#63564C414yescomplemented
24C2×C3×#97—31no—
25C2×#821—31no—
26C2×#821—31no—
27C2×#821—31no—
28C2×#821—61no—
29C2×#815D311yescharacteristic, complemented
30#4988—31no—
31#4984—31no—
32C2×#809—31no—
33#4939—31no—
34#4928—31no—
35C3×#340—31no—
36#4551—31no—
37#4551D311yescharacteristic, complemented
38#4529—31no—
39C23×C3⋊D3—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)C2×C412yes—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8D412yes—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3C2×C412yes—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66Dic3⋊Dic3—42no—
67#3722—42no—
68#3722—42no—
69#1936—91noSylow
70C22×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C22×C3×C8—21no—
74C22×C3×C8—31no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C2×D311yescharacteristic
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C42—31no—
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×C4×Dic3C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93C3×#97—62no—
94C3⋊#95—61no—
95C3⋊#95—61no—
96#821—34no—
97#821—64no—
98#821—62no—
99#821—62no—
100#815—22no—
101#809—34no—
102C23×C32C2×D411yescharacteristic
103C22×C3⋊D3—22no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—41no—
107C22×C3⋊D3—41no—
108C22×C3⋊D3—41no—
109C22×C3⋊D3—41no—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—22no—
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—41no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C32×C8—22no—
136C3×C3⋊C8—22no—
137C2×#102—91no—
138C2×#102—91no—
139C2×#97—31no—
140#390—91no—
141#389—91no—
142#340—31no—
143#340—91no—
144C23×D3—61no—
145C23×D3—61no—
146C23×D3—121no—
147C22×C3×C4—21no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×Dic3—21no—
155C22×Dic3—21no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3—121no—
159C22×Dic3D1211yescharacteristic
160C22×Dic3D1211yescharacteristic
161C2×D12—32no—
162C2×D12—32no—
163C2×D12—62no—
164C2×D12—62no—
165C2×D12—62no—
166C2×D12—61no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—121no—
177C2×D12—121no—
178C2×D12—121no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—22no—
184C2×C3×C8—32no—
185C2×C3×C8—41no—
186C2×C3×C8—41no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C2×C3×C8D1212yes—
190C2×C3×C8#6712yes—
191C3×C4⋊C4—32no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C42—61no—
196C3×C42—61no—
197(C2×D3)⋊C4—122no—
198(C2×D3)⋊C4—122no—
199(C2×D3)⋊C4—122no—
200(C2×D3)⋊C4—122no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—62no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—121no—
210C4⋊Dic3—122no—
211C4⋊Dic3C4×D312yes—
212Dic3⋊C4—122no—
213C4×Dic3—21no—
214C4×Dic3—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8C4×D312yes—
218C22×C32C4×D411yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32#12411yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C22×C32#13711yescharacteristic
225C2×C3⋊D3—42no—
226C2×C3⋊D3—42no—
227C2×C3⋊D3—42no—
228C2×C3⋊D3—81no—
229C2×C3⋊D3—81no—
230C2×C3⋊D3—81no—
231C2×C3⋊D3—81no—
232C32×C4#11711yescharacteristic
233C32×C4C4×D411yescharacteristic
234C32×C4#12311yescharacteristic
235C32×C4#12611yescharacteristic
236C3⋊Dic3—81no—
237C3×Dic3—42no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C22×D4—91no—
242C22×C8—31no—
243C22×C8D3211yescharacteristic
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—181no—
248C2×C22⋊C4—181no—
249C2×C22⋊C4—181no—
250C2×C42—31no—
251#102—94no—
252#102—182no—
253#97—62no—
254#95—181no—
255C23×C3—21no—
256C23×C3C2×D1211yescharacteristic
257C23×C3D3×D411yescharacteristic
258C22×D3—62no—
259C22×D3—62no—
260C22×D3—122no—
261C22×D3—122no—
262C22×D3—122no—
263C22×D3—121no—
264C22×D3—121no—
265C22×D3—121no—
266C22×D3—121no—
267C22×D3—121no—
268C22×D3—121no—
269C22×D3—121no—
270C22×D3—121no—
271C22×D3—121no—
272C22×D3—121no—
273C22×D3—121no—
274C22×D3—121no—
275C22×D3—241no—
276C22×D3—241no—
277C22×D3—241no—
278C22×D3—241no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—62no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4#23911yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—241no—
329C2×Dic3—241no—
330D12—64no—
331D12—62no—
332D12—62no—
333D12—62no—
334D12—62no—
335D12—122no—
336D12—122no—
337D12—122no—
338D12—121no—
339D12—121no—
340D12—121no—
341D12—121no—
342C3×C8—22no—
343C3×C8—22no—
344C3×C8—42no—
345C3×C8—62no—
346C3⋊C8—22no—
347C2×C32#38811yescharacteristic
348C2×C32#44011yescharacteristic
349C2×C32#44211yescharacteristic
350C2×C32#46811yescharacteristic
351C2×C32#46911yescharacteristic
352C2×C32#48911yescharacteristic
353C2×C32#49011yescharacteristic
354C3⋊D3—82no—
355C24—181no—
356C2×D4—92no—
357C2×D4—181no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—181no—
361C2×D4—181no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—32no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8#62612yes—
374C4⋊C4—32no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—362no—
381C22⋊C4—362no—
382C22⋊C4—362no—
383C42—61no—
384C42—61no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3C4×D1211yescharacteristic
393C22×C3#87511yescharacteristic
394C22×C3#67⋊C411yescharacteristic
395C22×C3#88511yescharacteristic
396C22×C3#89511yescharacteristic
397C22×C3#90811yescharacteristic
398C22×C3#90811yescharacteristic
399C22×C3#90811yescharacteristic
400C22×C3#90911yescharacteristic
401C22×C3#91111yescharacteristic
402C22×C3#91411yescharacteristic
403C22×C3#91411yescharacteristic
404C22×C3#91811yescharacteristic
405C22×C3#93011yescharacteristic
406C2×D3—124no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—242no—
414C2×D3—242no—
415C2×D3—242no—
416C2×D3—242no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—241no—
420C2×D3—241no—
421C2×D3—241no—
422C2×D3—241no—
423C2×D3—241no—
424C2×D3—241no—
425C2×D3—241no—
426C2×D3—241no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—121no—
432C3×C4—121no—
433C3×C4—122no—
434C3×C4—241no—
435C3×C4#87211yescharacteristic
436C3×C4C4×D1211yescharacteristic
437C3×C4#87611yescharacteristic
438C3×C4#88611yescharacteristic
439C3×C4#89211yescharacteristic
440C3×C4#89811yescharacteristic
441C3×C4C4×#6711yescharacteristic
442C3×C4#92911yescharacteristic
443Dic3—41no—
444Dic3—41no—
445Dic3—42no—
446Dic3—81no—
447Dic3—242no—
448Dic3—241no—
449Dic3—241no—
450C32#193611yescharacteristic, complemented, Sylow
451C23—182no—
452C23—361no—
453C23—361no—
454C23—361no—
455C23—361no—
456C23—361no—
457C23—361no—
458C23D3×D1211yescharacteristic
459D4—182no—
460D4—182no—
461D4—361no—
462D4—361no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—62no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4—361no—
478C2×C4#379811yescharacteristic
479C2×C4#379911yescharacteristic
480C2×C4C4×D3211yescharacteristic
481C2×C4#380411yescharacteristic
482C2×C4#380411yescharacteristic
483C2×C4C2×#62611yescharacteristic
484C8—22no—
485C8—62no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3#467011yescharacteristic
494C2×C3#471011yescharacteristic
495C2×C3#471111yescharacteristic
496C2×C3#471311yescharacteristic
497C2×C3#471411yescharacteristic
498C2×C3#476411yescharacteristic
499C2×C3#478511yescharacteristic
500C2×C3#479411yescharacteristic
501C2×C3#481711yescharacteristic
502C2×C3#486511yescharacteristic
503C2×C3#488611yescharacteristic
504C2×C3#494011yescharacteristic
505C2×C3#513411yescharacteristic
506C2×C3#513511yescharacteristic
507D3—244no—
508D3—242no—
509D3—242no—
510C22—362no—
511C22—362no—
512C22—362no—
513C22—721no—
514C22—721no—
515C22—721no—
516C22—721no—
517C22#6379411yescharacteristic
518C22#6379411yescharacteristic
519C22#6379511yescharacteristic
520C22#6380111yescharacteristic
521C22#6385211yescharacteristic
522C22#6388011yescharacteristic
523C22#6390911yescharacteristic
524C4—122no—
525C4—121no—
526C4—121no—
527C4—241no—
528C4—721no—
529C4#6383611yescharacteristic
530C4#6386811yescharacteristic
531C4C4×#62611yescharacteristic
532C4#6396611yescharacteristic
533C3—21no—
534C3#6885711yescharacteristic, complemented
535C3#6981811yescharacteristic, complemented
536C2—722no—
537C2#1059074611yescharacteristic
538C2#1059079511yescharacteristic
539C2#1059083511yescharacteristic
540C2#1059083811yescharacteristic
541C2#1059088211yescharacteristic
542C2#1059089311yescharacteristic
543C2#1059119411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1936
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#815C2semidirect
3. #10591352C2semidirect
6. C3×#4551C2semidirect
7. #10589164C2semidirect
23. #63564C4semidirect
29. C2×#815D3semidirect
37. #4551D3semidirect
450. C32#1936semidirect
534. C3#68857semidirect
535. C3#69818semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#636482
C2×C3×#8152
#105913522
#105913202
C2×#635642
C3×#45512
#105891642
#698183
#688573